Some applications, such as the positioning of optical elements as in interferometry, require extremely precise positioning such as with an accuracy of less than one micrometer. A lead screw and nut can be constructed with the required precision, and with a very small clearance such as 0.0005 inch, and a number 5 (five microinch) machine finish on the mating threads. However, even such elements will not provide the required precision and uniformity, or lack of "noise", in movement of the optical element. A positioning apparatus which could provide extreme precision in the movement of a nut and with an extremely small level of "noise", or unpredictable small sudden movements, in a clean environment in which instruments are utilized, would be of considerable value.